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Definition D866
Standard real logarithm function

Let $x \mapsto \log(x)$ be the D865: Standard natural real logarithm function.
The standard real logarithm function in base $a \in (0, \infty) \setminus \{ 1 \}$ is the D5482: Positive real function $$\log_a : (0, \infty) \to \mathbb{R}, \quad \log_a(x) = \frac{\log x}{\log a}$$

Let $x \mapsto \log_e(x)$ be the D865: Standard natural real logarithm function.
The standard real logarithm function in base $a \in (0, \infty) \setminus \{ 1 \}$ is the D5482: Positive real function $$\log_a : (0, \infty) \to \mathbb{R}, \quad \log_a(x) = \frac{\log_e x}{\log_e a}$$
Children
 ▶ Real entropy function
Results
 ▶ Change of base formula for logarithm function ▶ Homomorphism property of standard logarithm function ▶ Homomorphism property of standard logarithm function in the binary case ▶ Logarithm of a ratio ▶ Reflection property of standard logarithm function ▶ Standard logarithm of a positive real number raised to an integer power ▶ Value of standard logarithm function at its parameter value